HELSINKI, Finland — City boosters in this Nordic capital dream of a Guggenheim museum of Finnish wood rising near the Baltic Sea and one day drawing millions of tourists and cruise passengers. But the huge costs of the proposed development are stirring a backlash here against an institution that is ordinarily accustomed to eager suitors.

The proposal for the city of Helsinki to team up with the Solomon R. Guggenheim Foundation in New York to build a museum here is splitting politicians into camps of pro-business supporters seeking the wealth and attention that comes with an international brand, and Social Democrats and other left-of-center party members who are skeptical about shouldering the costs of a 130 million euro ($177 million) development deal.

The final decision will be determined largely by a yearlong open international architectural competition that began in June. Supporters hope the winner will impress critics with an innovative museum design for the site, on prime waterfront property on the South Harbor facing the heart of Helsinki and its neo-Classical buildings.

The project is part of an aggressive global effort by the Guggenheim to add to its museums in New York, Venice and Bilbao, Spain. A museum is scheduled to open in Abu Dhabi in 2017, and the Guggenheim is negotiating a new partnership with the Bilbao museum, whose existing contract with the foundation ends in December.

Each year the Guggenheim fields about a dozen requests from cities seeking a franchise for the halo effect of the Bilbao museum, which helped nurture the economy and tourism in the Basque region.

“We have to promote Helsinki, and that’s why we need some international brands like the Guggenheim,” said Jussi Pajunen, Helsinki’s mayor and the project’s chief promoter.

But the backlash against the project surprised the Guggenheim Foundation’s top executives. In 2011 critics began questioning the terms of the development deal, which would hand the Guggenheim most of the decision-making power but have the city shoulder all of the costs.

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Helsinki’s mayor, Jussi Pajunen, a supporter of a Guggenheim for his city, can view the proposed site from his office window. Above, Kaarin Taipale, an urban researcher who opposes the project.CreditTouko Hujanen for The New York Times

“I felt some defensiveness and some very developed hostility to us, a fear which I was empathetic toward — that the distinct local character of Helsinki would somehow be amalgamated into some sort of gigantic industrial apparatus,” said Richard Armstrong, the director of the foundation and the Guggenheim in New York.

Since the Helsinki proposal was announced more than three years ago, the Guggenheim Foundation has tenaciously promoted it despite critical setbacks, including the local city board’s rejection of the project in a narrow vote in 2012 because of cost concerns, particularly a controversial $30 million licensing fee for the privilege of using the Guggenheim name.

Newspaper polls at the time showed that a majority of city residents opposed the project. In the early stages, local artists balked at the idea that the existing Helsinki City Art Museum would be absorbed into the Guggenheim.

That idea was discarded when the Guggenheim returned with a retooled proposal in 2013, responding to some of the criticism. The foundation agreed not to charge the city its licensing fee but rather to help local supporters solicit private donations through a newly formed foundation. The later proposal also increased estimates of annual admission revenues and reduced by half the operation fees for the Guggenheim, to almost $1.4 million a year.

Not all the critics are satisfied. “This is like we are buying a Louis Vuitton bag because it is a famous brand — we need our own brands,” said Kaarin Taipale, a co-author of “In the Shadow of Guggenheim,” a book that analyzed the project. “The financing numbers have raised a lot of questions. They say we have different alternatives, but all are based on spending public money.”

Money is an important issue in Finland, which has been mired in recession for two years and is struggling with a decline in its electronics industry and a weakening of trade with its neighbor Russia. After the Guggenheim revised the proposal, the city board agreed to reconsider its stance but withhold a final decision until after the designs were evaluated.

When the design competition was announced last month, a Finnish television reporter asked Mr. Armstrong what alternatives he might pursue if the city or state refused to pay for the project. “These are typical bad questions,” he replied, and then walked out. Eventually he returned to resume the interview, but it was too late: The video of his remarks spread widely on the Internet, provoking accusations of arrogance.

“I was jet-lagged — I’m human,” Mr. Armstrong said later in a telephone interview. Today, though, he still shies away from discussing alternatives to Finnish funding: “That’s a wife-beater question, so I am not going to answer,” he said, adding: “We all have conditional situations that can develop in the future. I’m not sure how productive it is to be paralyzed by those fears.”

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Kaarin Taipale, an urban researcher who opposes the project.CreditTouko Hujanen for The New York Times

As in some other cities, Helsinki and its mayor are inspired by the success of the Guggenheim Bilbao in Spain, designed by Frank Gehry. Since it opened in 1997, the Basque region has been attracting nearly a million visitors a year, compared with fewer than 100,000 previously.

The museum in Helsinki could generate an economic impact of $56 million, creating nearly 500 jobs at the museum and locally, as well as 800 construction jobs, according to estimates by the Boston Consulting Group in a $2.9 million report financed by the city of Helsinki.

Much of the Guggenheim Bilbao’s popularity is attributed to its voluptuous, titanium-clad form. Mr. Armstrong said that while the design contest was stirring broad interest, it was not clear whether star architects like Mr. Gehry would take part. He added that the Helsinki design would probably be less flamboyant and have a smaller footprint than the Bilbao museum.

Some of the Guggenheim’s critics say the results of the design competition could prove helpful to them in weighing the merits against the costs. “We want to make sure this project benefits everybody,” said Emma Kari, who leads the Green Party members on the city board. “We will evaluate the estimates again. There are questions about the amount of people coming,” she said, describing an annual attendance estimate of 550,000 as “quite high.”

If that projection were to prove accurate, a Guggenheim museum would emerge as Finland’s most popular art site while also exceeding the volume of visitors at the Modern Museum in Stockholm.

The design competition is on a tight schedule, with the deadline for preliminary submissions set for September. Mikko Aho, a jury member and the director of city planning, said that while the designs were up to the competitors, all are expected to incorporate natural Finnish wood in some respect.

Ultimately, Mr. Armstrong of the Guggenheim is counting on the power of design to transform the rancorous debate into an enthusiastic one. “When the drawings come in for real buildings, there will be a gauge of what it will cost,” he said. “I am hopeful that moment will become catalytic.”

As for the museum site, he said, “To me it’s odd that in this supercharming, unusual place we have an asphalt parking lot.”

A version of this article appears in print on , on Page C1 of the New York edition with the headline: Helsinki Divided on Plan for a Guggenheim Satellite. Order Reprints | Today’s Paper | Subscribe